Robust least mean logarithmic square adaptive filtering algorithms

The conventional logarithm cost-based adaptive filters, e.g., the least mean logarithmic square (LMLS) algorithm, cannot combat impulsive noises at the filtering process. To address this issue, we present a novel robust least mean logarithmic square (RLMLS) algorithm by using a generalized logarithmic cost function. The proposed RLMLS algorithm can provide robustness against impulsive noises with the improvement of filtering accuracy. For theoretical analysis, the mean square analysis of RLMLS is provided in terms of the mean square deviation (MSD) and excess mean-square error (EMSE) with a white Gaussian reference. For further performance improvement in different noises, the variable step-size RLMLS (VSSRLMLS) based on the statistics of error is proposed to improve the convergence rate and steady-state mean square error, simultaneously. Analytical results and superiorities of RLMLS and VSSRLMLS in the context of system identification are supported by simulations from the aspects of filtering accuracy and robustness in Gaussian and impulse noises.     

A trust-region method for H2 model reduction of bilinear systems on the Stiefel manifold

This paper investigates the Riemannian trust-region method for H₂ model reduction of bilinear systems. The H₂ error norm is treated as a cost function on the Stiefel manifold such that the orthogonality constraint for the projection matrix is plainly satisfied. The property related to the Euclidean gradient is studied. Then, the inner product associated with the Riemannian Hessian is derived, which can simplify the expression of the trust-region subproblem. The trust-region method for H₂ model reduction is accordingly established and the convergence is further discussed. Finally, two numerical examples are employed to demonstrate the performance of the proposed method.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.     

Robust non-fragile filtering for networked systems with distributed variable delays

This paper is concerned with the robust non-fragile filtering for a class of networked systems with distributed variable delays. We model such a complex delay system with an augmented switched system. For the filtering implementation uncertainty, a stochastic variable is employed to indicate random occurrence of the filter gain change, and a norm bound to measure the change size. The suitably weighted measurements are proposed for filter performance improvement, instead of direct use of the measurements themselves which may have significant delays and degrade the performance. With some improved stability and l₂ gain analysis for the switched systems, a new sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and achieves a prescribed _H∞$H_{\infty }$ performance level. A numerical example is given to show the effectiveness of the proposed design.     

l1 filtering for continuous-discrete T-S fuzzy positive Roesser model

This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l₁ performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l₁-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.     

On convergence of the discrete-time nonlinear extended state observer

This paper concerns with the convergence of the discrete-time nonlinear extended state observer (ESO). Several kinds of discrete-time nonlinear ESO (NLESO) are proposed and then sufficient conditions based on linear matrix inequality (LMI) method are obtained to quantitatively reveal the relationship between the plant, the sampling interval, the parameter values of NLESO and its convergence. The theoretical results are verified by simulation using a motion control system. It shows that there may exist an optimal ω_o for a certain fixed sampling interval, and a smaller sampling interval generally generates better performance. What’s more, the proposed digital implementations of NLESO improve its performance over traditional Euler approximation discretization method.     

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper addresses the filtering problem for the one-sided Lipschitz nonlinear systems under measurement delays and disturbances using a generalized observer. A generalized architecture for filtering of the one-sided Lipschitz nonlinear systems with output delays is explored, which exhibits diverging manifolds, namely, the conventional static-gain filter and the dynamical filter, and can be employed to render robust stability of the filtering error dynamics. A matrix inequality based framework is obtained by employing a Lyapunov?Krasovskii (LK) functional, whose derivative is exploited through Jensen's inequality, one-sided Lipschitz condition, quadratic inner-boundedness inequality and range of the measurement delay, resulting into L₂ stability for the filtering error system. Generalized filter design for the Lipschitz nonlinear systems with delayed outputs and specific results for the delay-dependent and delay-rate-independent filtering schemes for the one-sided Lipschitz nonlinear systems are deduced from the proposed approach. Convex optimization techniques are employed to achieve a solution for the nonlinear constraints through linear matrix inequalities by employing cone complementary linearization approach. Illustrative numerical examples to demonstrate the effectiveness of proposed method are provided.     

Alternative convergence criteria for iterative methods of solving nonlinear equations

Let χ_m+1=T(χ_m) or even χ_m+1=T(χ_m,χ_m?1, …, χ_m?q), m=1,2,3 … be an iteration method for solving the nonlinear problem F(χ)=0, where F(χ) and its derivatives possess all of the properties required by T(χ_m). Then if it can be established that for the problem at hand ∥F(χ_m+1)∥?β_m∥F(χ_m)∥, ? m > M₀ (M₀<∞) and 0?β_m<1 , definitions are established and theorems proven concerning convergence, uniqueness and bounds on the error after ‘m’ successive iterations of a new approach to convergence properties T(χ_m). These charateristics are referred to as “alternate” (local, global) convergence properties and none of the proofs given are restricted to any specific type of method such as, e.g. contraction mapping types. Application of results obtained are illustrated using Newton's method as well as the general concept of Newton-like methods.     

Robust H∞ control for a class of uncertain nonlinear systems with mixed time-delays

This paper is concerned with the robust H_∞ control problem for a general class of uncertain nonlinear systems with mixed time-delays. The mixed time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is robustly stable for all admissible uncertainties with guaranteed H_∞ disturbance rejection attenuation level. By introducing a new Lyapunov–Krasovskii functional that reflects the mixed delays, sufficient conditions are established for the closed-loop system ensuring the robust stability as well as the H_∞ performance requirement. The controller design is facilitated in terms of the solvability of a Hamilton–Jacobi inequality. Two numerical examples are utilized to demonstrate the effectiveness of the proposed methods.     

H2/H∞ filtering for networked systems with data transmission time-varying delay,data packet dropout and sequence disorder

This paper investigates an H₂/H_∞ filter designing for networked systems perturbed by multiple noises. The measurement transmission from the sensor to the remote filter is completed via a communication network in simultaneously presenting of data transmission time-varying delays, data packet dropout and data sequence disorder. Since the filter will receive delayed and disordered information, a zero-order-hold (ZOH) or a logical-ZOH (LZOH) is firstly employed for resorting the chaos data sequence. Afterwards, a hybrid H₂/H_∞ filtering scheme is designed for accurately estimating the target output. By Itô formula and a novel free-weight method, the almost surely mean square exponentially stable (ASMSES) condition of the error system is conveniently obtained and the corresponding filter design method is finally presented. By the proposed method, not only the ASMSES with a pre-scheduled H₂/H_∞ performance can be achieved, but also the convergence rate of overall system is pre-regulable. In addition, it has been point out the dynamic filtering performance of LZOH scheme should be better than ZOH ones due to less time-varying delays are introduced and more latest measurement information are employed. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.     

Nonlinear H∞ robust control applied to F-16 aircraft with mass uncertainty using control surface inverse algorithm

In this paper, an analytic solution of nonlinear H_∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H_∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H_∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H_∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.     

Conjugate gradient-based FLANN algorithms in nonlinear active noise control

The conjugate gradient (CG) method exhibits fast convergence speed than the steepest descent, which has received considerable attention. In this work, we propose two CG-based methods for nonlinear active noise control (NLANC). The proposed filtered-s Bessel CG (FsBCG)-I algorithm implements the functional link artificial neural network (FLANN) as a controller, and it is derived from the Matérn kernel to achieve enhanced performance in various environments. On the basis of the FsBCG-I algorithm, we further develop the FsBCG-II algorithm, which utilizes the Bessel function of the first kind to constrain outliers. As an alternative, the FsBCG-II algorithm has reduced computational complexity and similar performance as compared to the FsBCG-I algorithm. Moreover, the convergence property of the algorithms is analyzed. The proposed algorithms are compared with some highly cited previous works. Extensive simulation results demonstrate that the proposed algorithms can achieve robust performance when the noise source is impulsive, Gaussian, logistic, and time-varying.     

Strong γc-γcl H∞ stabilization for networked control systems under denial of service attacks

This paper is concerned with the strong γ_c-γ_cl H_∞ stabilization problem for networked control systems (NCSs) subject to denial of service (DoS) attacks, which are common attack behaviors that affect the packet transmission of measurement or control signals. The purpose of the problem under consideration is to design a stable dynamic output feedback (DOF) controller (strong stabilizing controller) with the prescribed H_∞ performance norm bound γ_c to tolerate multiple packet dropouts caused by DoS attacks, such that, the closed-loop system is mean-square stable and captures the H_∞ disturbance attenuation norm bound γ_cl. Based on the Lyapunov functional and the stochastic control approach, some sufficient conditions with the form of matrix inequalities for the existence of the desired stable DOF controller are established. Then, by an orthogonal complement space technique, the controller gain is parameterized. Next, an iterative linear matrix inequality (LMI) algorithm is developed to obtain the controller gain. Finally, the usefulness of the proposed method is indicated by a numerical simulation example.     

H∞ filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations

In this paper, the problem of H_∞ filtering for neutral systems with mixed time-varying delays and nonlinear perturbations is investigated. Some new delay-dependent sufficient conditions are presented to ensure that the filtering error system is asymptotically stable with a prescribed level of H_∞ noise attenuation. In addition, the design procedures for the existence of such filter are presented in terms of a set of linear matrix inequalities (LMIs). Slack variables and convex combination technique are adopted to reduce the conservatism of obtained results. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.     

An event-triggered approach to distributed H∞ state estimation for state-saturated systems with randomly occurring mixed delays

In this paper, the event-triggered distributed H_∞ state estimation problem is investigated for a class of state-saturated systems with randomly occurring mixed delays over sensor networks. The mixed delays, which comprise both discrete and distributed delays, are allowed to occur in a random manner governed by two mutually independent Bernoulli distributed random variables. In order to alleviate the communication burden, an event-triggered mechanism is utilized for each sensor node to decide whether or not its current information should be broadcasted to its neighbors. The aim of this paper is to design event-triggered state estimators such that the error dynamics of state estimation is exponentially mean-square stable with a prescribed H_∞ performance index. By resorting to intensive stochastic analysis, sufficient conditions are first derived to guarantee the existence of the desired estimators, and the parameters of the desired distributed estimators are then obtained in light of the feasibility of a certain set of matrix inequalities. A numerical example is employed to illustrate the usefulness of the proposed distributed estimation algorithm.     

Design of mixed H2-dissipative observers with stochastic resilience for discrete-time nonlinear systems

A linear matrix inequality based mixed H₂-dissipative type state observer design approach is presented for smooth discrete time nonlinear systems with finite energy disturbances. This observer is designed to maintain H₂ type estimation error performance together with either H_∞ or a passivity type disturbance reduction performance in case of randomly varying perturbations in its gain. A linear matrix inequality is used at each time instant to find the time-varying gain of the observer. Simulation studies are included to explore the performance in comparison to the extended Kalman filter and a previously proposed constant gain observer counterpart.     

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H_∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H_∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.     

H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H_∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H_∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.     

Smoothed L1/2 regularizer learning for split-complex valued neuro-fuzzy algorithm for TSK system and its convergence results

This paper investigates an evolving split-complex valued neuro-fuzzy (SCVNF) algorithm for Takagi–Sugeno–Kang (TSK) system. In a bid to avoid the contradiction between boundedness and analyticity, splitting technique is traditionally employed to independently process the real part and the imaginary part of weight parameters in the system, which doubles weight dimension and causes oversized structure. For improving efficiency of structural optimization, previous studies have revealed that L_1/2-norm regularizer can be effective in such sparse tasks thus is regarded as a representative of L_q (0?<?q?<?1) regularizer. To eliminate oscillation phenomenon and stabilize training procedure, a smoothed L_1/2 regularizer learning is facilitated by smoothing the original one at the origin flexibly. It is rigorously proved that the real-valued cost function is monotonic decreasing during learning course, and the sum of gradient norm trends closer to zero. Plus some very general condition, the weight sequence itself is also convergent to a fixed point. Experimental results for the SCVNF are demonstrated, which match the theoretical analysis.